The Q-operator and functional relations of the eight-vertex model at root-of-unity μ = 2mK/N for odd N

Journal of Physics A: Mathematical and Theoretical

Volumn 40, Issue 36, 2007, Pages 11019-11044

  Roan, Shi Shyr ^a  

^a INSTITUTE OF MATHEMATICS   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548261728     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/40/36/004     Document Type: Article

References (37)

1. Andrews G E, Baxter R J and Forrester P J 1984 Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities J. Stat. Phys. 35 193-266
2. Albertini G, McCoy B M and Perk J H H 1989 Eigenvalue spectrum of the superintegrable chiral Potts model Advanced Studies in Pure Mathematics vol 19 (Tokyo/London: Kinokuniya/Academic) pp 1-55
3. Baxter R J 1971 Eight-vertex model in lattice statistics Phys. Rev. Lett. 26 832-3
4. Baxter R J 1971 One-dimensional anisotropic Heisenberg chain Phys. Rev. Lett. 26 834
5. Baxter R J 1972 Partition function of the eight vertex model Ann. Phys. 70 193-228
6. Baxter R J 1973 Eight-vertex model in lattice statistic and one-dimensional anisotropic Heisenberg chain: I. Some fundamental eigenvalues Ann. Phys. 76 1-24
7. Baxter R J 1973 Eight-vertex model in lattice statistic and one-dimensional anisotropic Heisenberg chain: II. Equivalence to a generalized ice-type lattice model Ann. Phys. 76 25-47
8. Baxter R J 1973 Eight-vertex model in lattice statistic and one-dimensional anisotropic Heisenberg chain: III. Eigenvalues of the transfer matrix and Hamiltonian Ann. Phys. 76 48-71
9. Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (New York: Academic)
10. Baxter R J 2002 Completeness of the Bethe ansatz for the six and eight-vertex models J. Stat. Phys. 108 1-48 (Preprint cond-mat/0111182)
11. Baxter R J, Bazhanov V V and Perk J H H 1990 Functional relations for transfer matrices of the chiral Potts model Int. J. Mod. Phys. B 4 803-70
12. Bazhanov V V and Mangazeev V V 2007 Analytic theory of the eight-vertex model Nucl. Phys. B 775 225-82 (Preprint hep-th/0609153)
13. Date E, Jimbo M, Kuniba A, Miwa T and Okado M 1986 Fusion of the eight vertex SOS model Lett. Math. Phys. 12 209-15
14. Date E, Jimbo M, Kuniba A, Miwa T and Okado M 1987 Lett. Math. Phys. 14 97 (erratum and addendum)
15. Date E, Jimbo M, Kuniba A, Miwa T and Okado M 1988 Exactly solvable SOS models: II. Proof of the star-triangle relation and combinatorial identities Proc. Conformal Field Theory and Solvable Lattice Models (Kyoto, 1986) Adv. Stud. Pure Math. 16 (Boston, MA: Academic Press) 17-122
16. 2 loop algebra symmetry for the six-vertex model at roots of unity J. Stat. Phys. 102 701-36 (Preprint cond-mat/9912141)
17. Deguchi T 2002 Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix J. Phys. A: Math. Gen. 35 879-95 (Preprint cond-mat/0109078)
18. 2 loop algebra symmetry of the six-vertex model at roots of unity Int. J. Mod. Phys. B 16 1899-905 (Preprint cond-mat/0110121)
19. 2 loop algebra at roots of unity Preprint cond-mat/0503564
20. 2) Nucl. Phys. B 480 485-503
21. 2) Commun. Math. Phys. 181 741-61
22. Fabricius K and McCoy B M 2001 Bethe's equation is incomplete for the XXZ model at roots of unity J. Stat. Phys. 103 647-78 (Preprint cond-mat/0009279)
23. Fabricius K and McCoy B M 2001 Completing Bethe equations at roots of unity J. Stat. Phys. 104 573-87 (Preprint cond-mat/0012501)
24. Fabricius K and McCoy B M 2002 Evaluation Parameters and Bethe Roots for the Six Vertex Model at Roots of Unity (Progress in Mathematical Physics) vol 23 ed M Kashiwara and T Miwa (Boston: Birkhäuser) pp 119-44 (Preprint cond-mat/0108057)
25. Fabricius K and McCoy B M 2003 New developments in the eight vertex model J. Stat. Phys. 111 323-37 (Preprint cond-mat/0207177)
26. Fabricius K and McCoy B M 2004 Functional equations and fusion matrices for the eight vertex model Publ. RIMS 40 905-32 (Preprint cond-mat/0311122)
27. Fabricius K and McCoy B M 2005 New developments in the eight vertex model: II. Chains of odd length J. Stat. Phys. 120 37-70 (Preprint cond-mat/0410113)
28. Fabricius K and McCoy B M 2004 Root of unity symmetries in the 8 and 6 vertex models Preprint cond-mat/0411419
29. Fabricius K and McCoy B M 2006 An elliptic current operator for the eight-vertex model J. Phys. A: Math. Gen. 39 14869-86 (Preprint cond-mat/0606190)
30. Fabricius K 2006 A new Q-operator in the eight-vertex model Preprint cond-mat/0610481v3
31. Roan S S 2005 Chiral Potts rapidity curve descended from six-vertex model and symmetry group of rapidities J. Phys. A: Math. Gen. 38 7483-99 (Preprint cond-mat/0410011)
32. (j)- matrices in the superintegrable chiral Potts model J. Stat. Mech. P09007 (Preprint cond-mat/0505698)
33. Roan S S 2006 Bethe ansatz and symmetry in superintegrable chiral Potts model and root-of-unity six-vertex model Nankai Tracts in Mathematics Vol 10: Differential Geometry and Physics ed M L Go and W Zhang (Singapore: World Scientific) pp 399-409 (Preprint cond-mat/0511543)
34. Roan S S 2006 The Q-operator for root-of-unity symmetry in six vertex model J. Phys. A: Math. Gen. 39 12303-25 (Preprint cond-mat/0602375)
35. Roan S S 2007 Fusion operators in the generalized n(2)-model and root-of-unity symmetry of the XXZ spin chain of higher spin J. Phys. A: Math. Theor. 40 1481-511 (Preprint cond-mat/0607258)
36. Takhtadzhan L A and Faddeev L D 1979 The quantum method of the inverse problem and Heisenberg XYZ model Usp. Mat. Nauk 34 13-63 (in Russian)
37. Takhtadzhan L A and Faddeev L D 1979 Russ. Math. Surv. 34 11-68 (Engl. Transl.)